Question

Hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually. What multiplicative rate of change should Hal use in his function?

0.02
0.98
1.02
1.98

Answer 1

Answer:

0.98

Step-by-step explanation:

Explanation

The investment of $10,000 decreases by 2% every year. So the following year is usually (100 - 2)=98% of the previous year. This is a geometric progression.

In this case the first term = 10000

The second term = 98% × 10000 = 9800.

The common ratio = 9800/10000=49/50

The multiplicative rate of change that should be in Hal’s function = 49/50=0.98.

The equation of the exponential rate would be;

10,000ₓ0.98ⁿ.

where n is the number years.

Answer 2

The multiplicative rate of change that Hal should use in his function is 0.98

The standard exponential equation is given as $y=ab^x$

• a is the intercept of the graph
• b determines whether the investment is increasing or decreasing.

Since the value of a $10,000 investment decreases by 2% annually, the multiplicative rate of change will be:

• multiplicative rate = 100 - 2
• multiplicative rate = 98% = 0.98

The resulting exponential function will be $y = 10000(0.98)^x$

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